Let P(n) be the formula(adsbygoogle = window.adsbygoogle || []).push({});

1^2 + 2^2 + ... + n^2 = n(n +1)(2n +1)/6

a. Write P, is it true?(1)

1^2 + 2^2 + ... + 1^2 = 1(1 +1)(2(1) +1)/6 =

1^2 + 2^2 + ... + 1^2 = 1(1 +1)(2 +1)/6

LHS = 1^2 = 1

RHS = 2 . 3/6 = 1 True

b. Write P(k)

Basis Step

n = k

1^2 + 2^2 + ... + k^2 = k(k +1)(2k +1)/6

c. Write P(k+1)

Inductive step

n = k then n = k + 1

1^2 + 2^2 + ... + (k+1)^2 = (k+1)((k+1) +1)(2(k+1)+1)/6

Now this is where I get confused with induction writing the proof of the inductive step.

d. use mathematical induction to prove k then k+1, n>_1

1^2 + 2^2 + ... + (k+1)^2 = (k+1)((k+1) +1)(2(k+1)+1)/6

LHS = (k+1)^2

= k+1

= k

= 1

RHS = (k+3)+1(2+1)/6 combining like terms

= (k+3)+(2+1)/6

= 3k+3/6

= 6k/6

= k

= 1

Is this the kind of working that is valid? it seems right to me.

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# Mathimatical Induction

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